Problem: Simplify. Rewrite the expression in the form $a^n$. $a^{5}\cdot a^{-3}=$
Solution: Recall that $x^n\cdot x^m=x^{n+m}$. $\begin{aligned} (a^{5})(a^{-3})&=a^{5+(-3)} \\\\ &= a^{5-3} \\\\ &= a^{2} \end{aligned}$